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Advanced Artificial Lift Methods – PE 571 Chapter 1 - Electrical Submersible Pump

Advanced Artificial Lift Methods – PE 571 Chapter 1 - Electrical Submersible Pump Centrifugal Pump Theory – Inviscid Fluids – Single Phase. Theoretical Head Developed by an Impeller. Principles of an Centrifugal Pump.

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Advanced Artificial Lift Methods – PE 571 Chapter 1 - Electrical Submersible Pump

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  1. Advanced Artificial Lift Methods – PE 571 Chapter 1 - Electrical Submersible Pump Centrifugal Pump Theory – Inviscid Fluids – Single Phase

  2. Theoretical Head Developed by an Impeller Principles of an Centrifugal Pump ESPs are multi stage centrifugal pumps. The two main components of a centrifugal pump are the impeller and the diffuser. The Impeller takes the power from the rotating shaft and accelerates the fluid. The diffuser transforms the high fluid velocity (kinetic energy) into pressure.

  3. Theoretical Head Developed by an Impeller Geometry of an Centrifugal Pump Impeller Washer Diffuser The main components of an ESP including:

  4. Theoretical Head Developed by an Impeller Geometry of an Centrifugal Pump Impeller Impeller Diffuser Diffuser

  5. Theoretical Head Developed by an Impeller True Velocity Profile of Fluid Inside an Impeller

  6. Theoretical Head Developed by an Impeller Assumptions Assumptions: Two dimensions: radial and tangential direction. The impeller passages are completely filled with the flowing fluid at all time (no void spaces) The streamlines have a shape similar to the blade’s shape Incompressible, inviscid, and single phase fluid The velocity profile is sysmetric. The head calculated based on these assumptions is known as the theoretical head

  7. Theoretical Head Developed by an Impeller Velocities at the intake and outlet of an impeller

  8. Theoretical Head Developed by an Impeller Velocities at the intake and outlet of an impeller Exit Velocity Triangle Entrance Velocity Triangle

  9. Theoretical Head Developed by an Impeller Velocity at One Point on the Impeller’s Blade

  10. Theoretical Head Developed by an Impeller Velocity at One Point on the Impeller’s Blade

  11. Theoretical Head Developed by an Impeller Velocity at One Point on the Impeller’s Blade

  12. Theoretical Head Developed by an Impeller Triangle Fluid Velocity

  13. Theoretical Head Developed by an Impeller Conclusion on Triangle Fluid Velocity Known 3 operational parameters: 1. Angle, b: knowing pump blade geometry 2. Tangential velocity, U: knowing the rotational speed 3. Radial velocity, vr: knowing the flow rate. Therefore, the velocity triangle is completely determined. What we need now is to find the pressure increment developed by one impeller as a function of those 3 operational parameters and the fourth one, namely the fluid density

  14. Theoretical Head Developed by an Impeller Based on a Free Body Diagram R + dr r

  15. Theoretical Head Developed by an Impeller Based on a Free Body Diagram

  16. Theoretical Head Developed by an Impeller Based on a Free Body Diagram

  17. Theoretical Head Developed by an Impeller Based on a Free Body Diagram

  18. Theoretical Head Developed by an Impeller Based on a Free Body Diagram

  19. Theoretical Head Developed by an Impeller Mass Balance Mass balance equation under steady state conditions in cylindrical coordinate: Note that the fluid at the outlet of the impeller has two components: vr and vq. However, the change of vq respect to q is zero. Hence: constant

  20. Theoretical Head Developed by an Impeller Mass Balance The flow rate entering the pump intake is given (ri = r): or Rotational speed is related to the tangential velocity U by: Hence, we know three parameters:

  21. Theoretical Head Developed by an Impeller Mass Balance Three parameters: Combining with the triangle velocity gives:

  22. Theoretical Head Developed by an Impeller Momentum Equation For S.S; incompressible and single phase fluid; the momentum equations in the cylindrical coordinates are given:

  23. Theoretical Head Developed by an Impeller Total Pressure Losses Along the Streamline If the fluid is inviscid; No change of velocity in z and q (symmetric velocity) direction; Neglect the pressure drop due to gravity: Total derivative of pressure respect to the radius: Therefore: Streamline Trajectory

  24. Theoretical Head Developed by an Impeller Streamline Geometric Relationship

  25. Theoretical Head Developed by an Impeller Total Pressure Losses Along the Streamline Therefore, the total pressure losses along the streamline can be express as: From the triangle geometric relationship: Hence:

  26. Theoretical Head Developed by an Impeller Total Pressure Losses Along the Streamline Simplifying this equation gives

  27. Theoretical Head Developed by an Impeller Total Pressure Losses Along the Streamline Finally, the pressure difference across a streamline is given: Integrate this equation gives the pressure increase across one stage: By definition: Hence:

  28. Theoretical Head Developed by an Impeller Total Pressure Losses Along the Streamline Using the geometrical relationships: This equation can be expressed as the Euler Equation: Field unit:

  29. Theoretical Head Developed by an Impeller Total Pressure Losses Along the Streamline

  30. Theoretical Head Developed by an Impeller Pump Head Definition Definition for the pump head: Head is an indirect measurement of pressure that does not depend on the fluid density. That means for low viscous fluids, the pump performance can b uniquely defined in terms of head. In other words, the pump performance, in pressure, depends on the density of the fluid being pumped, but when this performance is expressed in head, the pump performance is independent of the fluid being pumped

  31. Theoretical Head Developed by an Impeller Pump Head Definition

  32. Theoretical Head Developed by an Impeller Head Losses Due to the Leakage and recirculation of fluid inside the impleller. Hydraulic losses including: Diffusion loss due to divergence, or convergence Fluid shock loss at the inlet Mixing and eddying loss at the impeller discharge Turning loss due to turning of the absolute velocity vector Separation losses Friction losses Mechanical losses

  33. Theoretical Head Developed by an Impeller Leakage and Recirculation Losses Recirculation Leakage

  34. Theoretical Head Developed by an Impeller Leakage and Recirculation Losses Theoretical diagram Diagram with recirculation

  35. Theoretical Head Developed by an Impeller Leakage and Recirculation Losses Theoretical head (Euler head) Head, H Leakage/Recirculation losses Flow rate, Q

  36. Theoretical Head Developed by an Impeller Hydraulic Losses Pumps are designed trying to achieve a no pre-rotation condition close to the best efficiency point, since this condition minimize shock-losses. In other words, shock losses increase as we move away from the BEP.

  37. Theoretical Head Developed by an Impeller Hydraulic Losses Theoretical head (Euler head) Head, H Hydraulic losses Other losses including friction, mixing, change in direction of fluid, separation, etc. also contribute significantly to the total losses due to hydraulic. Flow rate, Q

  38. Theoretical Head Developed by an Impeller Friction Losses Theoretical head (Euler head) Head, H Friction losses Friction losses increases with increasing flowrate and viscosity. Flow rate, Q

  39. Theoretical Head Developed by an Impeller Mechanical Losses These losses include disk friction and frictional losses in bearings. The most significant loss is the thrust bearing loss. The mechanical losses do not have any effect on head and capacity of a pump but increase the brake hoursepower.

  40. Theoretical Head Developed by an Impeller Total Losses Theoretical head (Euler head) Hydraulic losses Friction losses Head, H Actual Head Leakage/Recirculation losses Flow rate, Q

  41. Theoretical Head Developed by an Impeller Horsepower The hydraulic horsepower is the energy transmitted to the fluids by the pump. The break horsepower is the energy required by the pump shaft to turn. Some of this energy is dissipated inside the pump. The ratio between the hydraulic horsepower and the break horsepower is the pump hydraulic efficiency.

  42. Theoretical Head Developed by an Impeller Pump Performance In practice, a pump is tested by running it at a constant speed and varying the flow by controlling the choke. During the test, Q, DP, and the break horsepower are measure at several points. The DP is then converted to head and the overal efficiency of the pump is calculated. Based on these data, we can develop the pump performance. The performance curve of a centrifugal pump can be summarized in only one curve of head vs. flowrate for all low viscous fluids.

  43. Theoretical Head Developed by an Impeller Pump Performance

  44. Theoretical Head Developed by an Impeller Pump Performance Manufacturers also provide polynomial equations to describe the catalog pump performance curves.

  45. Theoretical Head Developed by an Impeller Pump Performance Do the calculation for these correlations:

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